Two observers calculate the trace anomaly

Capri, Anton Z; Kobayashi, Masanori; Lamb, David J.

doi:10.1088/0264-9381/13/2/006

Cited by 6 publications

(12 citation statements)

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“…However, in the corresponding quantized theory the stress tensor may acquire a nonvanishing trace through renormalization (this is called conformal or trace anomaly) [6,7]. In two dimensions, the trace T α α can only be proportional to the Ricci scalar R of the theory [8,40]. This is in agreement with Wald's axioms.…”

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confidence: 71%

Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

Vagenas

2003

Phys. Rev. D

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We treat the two-dimensional Achucarro-Ortiz black hole (also known as (1 + 1) dilatonic black hole) as a Casimir-type system. The stress tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional "walls" ("Dirichlet walls") is explicitly calculated in three different vacua. Without employing known regularization techniques, the expression in each vacuum for the stress tensor is reached by using the Wald's axioms. Finally, within this asymptotically non-flat gravitational background, it is shown that the equilibrium of the configurations, obtained by setting Casimir force to zero, is controlled by the cosmological constant.

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confidence: 71%

Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

Vagenas

2003

Phys. Rev. D

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“…and that F is the same as F , up to an additive constant that drops out of the derivatives appearing in Eqs. (45) and (58). Furthermore, one can readily calculate that, analogous to Eqs.…”

Section: Covariant Forms For the Stress Tensor And Conformal Invarmentioning

confidence: 96%

“…The research for this paper was motivated by my attempt to understand a recent paper by Capri, Kobayashi, and Lamb [45]. (In particular, it justifies their assumption that the energy density and flux are zero for the instantaneous vacuum of a geodesic Cauchy line, but only when it has infinite length.)…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…again with the two signs independent. For a spacetime of topology R 1 × S 1 , the one-form ω that determines the stressenergy tensor (45) gives two conformal invariants of the quantum state, each a nonlocal functional of the geometry and of the stress-energy tensor field:…”

Section: Covariant Forms For the Stress Tensor And Conformal Invarmentioning

confidence: 99%

“…For a state which is not the instantaneous vacuum for any choice of Cauchy line and for any conformally transformed metric, E u and/or E v are positive. [Neither one can be negative for the stress-energy tensor arising from a quantum state of a set of fields with the corresponding value of ǫ, though one can certainly choose an (imaginary) ω, and hence an artificial conserved stress-energy tensor (45) with the correct trace but with E u and/or E v arbitrarily negative. Analogously, one can write down in Minkowski spacetime a covariantly constant (and hence conserved) artificial stress-energy tensor that has a constant negative energy density everywhere, but one cannot get such a tensor as the expectation value of the regularized stress-energy tensor operator in any quantum state.]…”

Section: Covariant Forms For the Stress Tensor And Conformal Invarmentioning

confidence: 99%

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Stress tensors for instantaneous vacua in dimensions

Page¹

1997

Class. Quantum Grav.

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The regularized expectation value of the stress-energy tensor for a massless bosonic or fermionic field in 1+1 dimensions is calculated explicitly for the instantaneous vacuum relative to any Cauchy surface (here a spacelike curve) in terms of the length L of the curve (if closed), the local extrinsic curvature K of the curve, its derivative K ′ with respect to proper distance x along the curve, and the scalar curvature R of the spacetime:in an orthonormal frame with the spatial vector parallel to the curve. Here ǫ = 1 for an untwisted (i.e., periodic in x) one-component massless bosonic field or for a twisted (i.e., antiperiodic in x) two-component massless fermionic field, ǫ = − 1 2 for a twisted one-component massless bosonic field, and ǫ = −2 for an untwisted two-component massless fermionic field. The calculation uses merely the energy-momentum conservation law and the trace anomaly (for which a very simple derivation is also given herein, as well as the expression for the Casimir energy of bosonic and fermionic fields twisted by an arbitrary amount in R D−1 × S 1 ). The two coordinate and conformal invariants of a quantum state that are (nonlocally) determined by the stress-energy tensor are given. Applications to topologically modified deSitter spacetimes, to a flat cylinder, and to Minkowski spacetime are discussed. * Alberta-Thy-02-96, gr-qc/9603005 † Internet address: don@phys.ualberta.ca

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Casimir Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

Wang

Yang

2007

Int J Theor Phys

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A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively. The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms, the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density, and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy, Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after radiation.KEY WORDS: casimir effect; two dimensional black hole; global monopole. PACS: 42.50.Lc.

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Two observers calculate the trace anomaly

Cited by 6 publications

References 5 publications

Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

Stress tensors for instantaneous vacua in dimensions

Casimir Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

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